I have both DS and gp2x with headphone plugs that have only one of the two pins left

when I insert headphones to DS, I can hear sounds with only one headphone, other one is mute and speakers will turn off
When I insert them to gp2x, speakers will stay half on and other headphone will be half on

so, is this hardware problem or firmware?

(sry for my bad english)

I think that you should get a new set of phones

look at the headphone "hole". you will see 2 pins, one at left side and one at right side.
I have got only one, another one is missing

Well , then it's evidently a hardware issue , send it back if it's under guarantee, or, if you have enough experience, open the GP2X and perform surgery, it may be that the actual 'pin' is simply bent and is still in place ?.

It is not in there.
my DS has the same thing, but it can turn off the speakers, gp2x will leave them half on

Check this thread out: http://www.gp32x.com/board/index.php?showtopic=24004

mine is different, my gp2x worked but I broke it, I have broken DS too but I gues that DS is better...

I think there's a software hack to manually shut off the speakers, but like you said, it's broken... you should have it replaced.